Tack lockers will not stop your tack from molding, it might actually increase it.
Tack "molds" from...
Molds and mildews are fungus.
All mildews are mold, but not all molds are mildews
Either way - molds and mildews are common in dark, damp, humid, poorly ventilated areas.
That is what you will create by building and putting your tack in a tack locker with minimal ventilation...
Better to secure your tack in a way that it is able to breathe, be in a ventilated and light area not locked away in the dark and dank of a box.
Maybe construct something with strong wire mesh if you need to secure your equipment and store things away than solid wood sided lockers...do it with wood frame and heavy metal wire instead...
I would store nothing "edible" in plastic as mice gnaw through plastic with no problem... they get into feed, storage containers...pretty much anything not metal if they choose to..it is only a matter of time and their nose to smell out the desired gnaw toy to them.
You can try mothballs and or cedar pieces that repel moths. They may also help repel those pesky mice from looking for a easy meal or soft bed at your expense.